Spatial Modeling of Housing Prices
- Goal: estimate housing prices in Hennepin and Ramsey county, Minneapolis, Minnesota using the BYM spatial model with R-INLA packages.
Housing Price Data in Hennepin and Ramsey county, Minneapolis, Minnesota
The Hennepin and Ramsey housing prices are gathered aggregate summaries of the people who live in Hennepin and Ramsey county, summarized for each census tract based on data from 2015-2019 American Community Service run by the U.S. Census Bureau. A census tract is a statistical subdivision of a county that aims to have roughly 4,000 inhabitants and they are intended to be fairly homogeneous with respect to demographic and economic conditions. #need revision
load('SpatialData.RData')
ggplot(mn_data, aes(x=HouseValueE))+
geom_density()
This dataset contains housing data of 464 Hennepin and Ramsey census tracts including median prices of housing in USD (HouseValueE), median household income in the past 12 months (in 2019 inflation) (IncomeE), and average household size of occupied houses (HouseholdSizeE). We create the variable called vble with the logarithm of the median prices to put it in the same scale, and map the log price using mapview (Figure 1). The map suggests that the housing prices are greater in the southwest, and prices are related to those in neighboring areas. Noted that the empty area is the University of Minnesota area, since there is no houses listed.
Figure 1 Logarithm of housing prices in Hennipin & Ramsey county, MN per census tract from the spData package
We will model the logarithm of the median prices using as covariates the average Median household income in the past 12 months (IncomeE) and the average household size (HouseholdSizeE). Figure 2 shows the relationships between pairs of variables visualized using the ggpairs() function of the GGally package (Schloerke et al. 2021). We observe a negative relationship between the logarithm of housing price and crime, and a positive relationship between the logarithm of housing price and the average number of rooms.
Figure 2 Relationship betwen the outcome variable logarithm of housing price (vble), and the average Median household income in the past 12 months (IncomeE) and the average household size (HouseholdSizeE)
# Find relationship of crime rate and number of rooms with log(house price)
ggpairs(data = mn_data, columns = c("vble", "HouseholdSizeE", "IncomeE"))
Model
Let \(Y_i\) be the logarithm of housing price of area \(i\), \(i = 1 , \dots, n\). We fit a BYM model that considers \(Y_i\) as the response variable, and household income and household size as covariates: \[ Y \sim N(\mu_i,\sigma^2), i = 1, \dots, n \\ \mu_i=\beta_0+\beta_1 \times Income+\beta_2 \times HouseholdSize + u_i+v_i \] where, (Question? does this mean that each household has a seperate intercept) - \(\beta_0\): the global intercept, which every household will have the same intercept. - \(\beta_1\), \(\beta_2\): represent respectively, the coefficients of the covariates household income and household size. - \(\mu_i\): a spatially structured effect modeled with a CAR structure,\(\mu_i| u_{-i} \sim N(\mu_{\delta_i}, \frac{\sigma^2_u}{n_{\delta_i}})\). - \(v_i\): an unstructured effect modeled as \(v_i \sim N(\theta, \sigma^2_v)\).
Neighborhood Matrix
We decided to use Queen neighborhood structure, which …
Figure 3 Neighborhood Network Structure
In the model, the spatial random effect \(u_i\) needs to be specified using a neighborhood structure. As we mentioned in the spatial model section, there are 3 commmon neighborhood structure: Queen, Rook, and Bishop. Here, we assume two areas are neighbors if they share a common edge or a common vertex. We create a neighborhood structure using functions of the spdep package (Bivand 2022).
First, we use the poly2nb() function to generate a spatial weights matrix (nb) based on the data (mn_data) and using queen contiguity to define neighborhood relationships between polygons. Each element of the list nb represents one area and contains the indices of its neighbors. For example, nb[[1]] contains indices of neighboring polygons in area 1.
[[1]]
[1] 50 64 122 177 241 423 457
[[2]]
[1] 145 180 276 339 365
[[3]]
[1] 128 266 337 385 463Figure 3 shows a map with the neighbors obtained. This plot is obtained by first plotting the map of Ramsey and Hennipin, and then overlapping the queen neighborhood structure with the plot.nb() function passing the neighbor list and the coordinates of the map.
plot(st_geometry(mn_data), border = "black")
plot.nb(nb, st_geometry(mn_data), add = TRUE)
To construct the neighborhood matrix that can be used in the INLA function, we use the nb2INLA() function to convert the nb list into a file called map.adj. This step will make sure that we have the representation of the neighborhood matrix as required by R-INLA. The map.adj file is saved in the working directory which can be obtained with getwd(). Then, we read the map.adj file using the inla.read.graph() function of R-INLA, and store it in the object g which we later use to specify the spatial model using R-INLA.
nb2INLA("map.adj", nb)
g <- inla.read.graph(filename = "map.adj")
mn_data$re_u <- 1:nrow(mn_data)
mn_data$re_v <- 1:nrow(mn_data)
prior <- list(
prec = list(
prior = "pc.prec",
param = c(0.5 / 0.31, 0.01)),
phi = list(
prior = "pc",
param = c(0.5, 2 / 3))
)
# Specify BYM model
formula <- vble ~
f(re_u, model = "besag", graph = g, scale.model = TRUE) +
f(re_v, model = "iid")
formula <- vble ~ f(re_u, model = "bym2", graph = g, hyper = prior)
res <- inla(formula, family = "gaussian", data = mn_data,
control.predictor = list(compute = TRUE),
control.compute = list(return.marginals.predictor = TRUE))
res$summary.fixed mean sd 0.025quant 0.5quant 0.975quant
(Intercept) 12.70831 0.0004635248 12.70734 12.70831 12.70928
mode kld
(Intercept) 12.70831 0.0006254889summary(res$summary.fitted.values) mean sd 0.025quant 0.5quant
Min. :11.89 Min. :0.009514 Min. :11.87 Min. :11.89
1st Qu.:12.47 1st Qu.:0.009533 1st Qu.:12.45 1st Qu.:12.47
Median :12.68 Median :0.009537 Median :12.66 Median :12.68
Mean :12.71 Mean :0.009543 Mean :12.69 Mean :12.71
3rd Qu.:12.92 3rd Qu.:0.009543 3rd Qu.:12.90 3rd Qu.:12.92
Max. :13.94 Max. :0.009846 Max. :13.92 Max. :13.94
0.975quant mode
Min. :11.91 Min. :11.89
1st Qu.:12.49 1st Qu.:12.47
Median :12.70 Median :12.68
Mean :12.73 Mean :12.71
3rd Qu.:12.94 3rd Qu.:12.92
Max. :13.96 Max. :13.94 # Posterior mean and 95% CI
mn_data$PM <- res$summary.fitted.values[, "mean"]
mn_data$LL <- res$summary.fitted.values[, "0.025quant"]
mn_data$UL <- res$summary.fitted.values[, "0.975quant"]mapsf <- st_as_sf(mn_data)
gRR <- ggplot(mn_data) + geom_sf(aes(fill = PM)) +
scale_fill_gradient2( midpoint = 12.5,low = "blue", high = "red") +
theme_bw()
gLL <- ggplot(mn_data) + geom_sf(aes(fill = LL)) +
scale_fill_gradient2(midpoint = 12.5, low = "blue", high = "red") +
theme_bw()
gUL <- ggplot(mn_data) + geom_sf(aes(fill = LL)) +
scale_fill_gradient2(midpoint = 12.5, low = "blue", high = "red") +
theme_bw()
library(cowplot)
plot_grid(gRR, gLL, gUL, ncol = 1)
# common legend
at <- seq(min(c(mn_data$PM, mn_data$LL, mn_data$UL)),
max(c(mn_data$PM, mn_data$LL, mn_data$UL)),
length.out = 8)
# popup table
popuptable <- leafpop::popupTable(dplyr::mutate_if(mn_data,
is.numeric, round, digits = 2),
zcol = c("NAME", "vble", "HouseholdSizeE", "IncomeE", "PM", "LL", "UL"),
row.numbers = FALSE, feature.id = FALSE)
m1 <- mapview(mn_data, zcol = "PM", map.types = "CartoDB.Positron",
at = at, popup = popuptable)
m2 <- mapview(mn_data, zcol = "LL", map.types = "CartoDB.Positron",
at = at, popup = popuptable)
m3 <- mapview(mn_data, zcol = "UL", map.types = "CartoDB.Positron",
at = at, popup = popuptable)
m <- leafsync::sync(m1, m2, m3, ncol = 3)
m# Transformation of the marginal of
# the first area with inla.tmarginal()
# inla.tmarginal(function(x) exp(x),
# res$marginals.fitted.values[[1]])
# Transformation marginals with inla.tmarginal()
marginals <- lapply(res$marginals.fitted.values,
FUN = function(marg){inla.tmarginal(function(x) exp(x), marg)})
# Obtain summaries of the marginals with inla.zmarginal()
marginals_summaries <- lapply(marginals,
FUN = function(marg){inla.zmarginal(marg)})Mean 306296
Stdev 2900.27
Quantile 0.025 300290
Quantile 0.25 304767
Quantile 0.5 306245
Quantile 0.75 307748
Quantile 0.975 312635
Mean 350380
Stdev 3315.76
Quantile 0.025 343317
Quantile 0.25 348663
Quantile 0.5 350368
Quantile 0.75 352074
Quantile 0.975 357434
Mean 219331
Stdev 2076.56
Quantile 0.025 214974
Quantile 0.25 218246
Quantile 0.5 219308
Quantile 0.75 220381
Quantile 0.975 223814
Mean 260598
Stdev 2467.64
Quantile 0.025 255511
Quantile 0.25 259293
Quantile 0.5 260548
Quantile 0.75 261829
Quantile 0.975 266015
Mean 193449
Stdev 1831.12
Quantile 0.025 189639
Quantile 0.25 192486
Quantile 0.5 193421
Quantile 0.75 194369
Quantile 0.975 197434
Mean 260214
Stdev 2462.97
Quantile 0.025 255011
Quantile 0.25 258932
Quantile 0.5 260195
Quantile 0.75 261465
Quantile 0.975 265497
Mean 529419
Stdev 5004.63
Quantile 0.025 518685
Quantile 0.25 526839
Quantile 0.5 529420
Quantile 0.75 531991
Quantile 0.975 539990
Mean 192829
Stdev 1825.09
Quantile 0.025 189003
Quantile 0.25 191875
Quantile 0.5 192809
Quantile 0.75 193752
Quantile 0.975 196773
Mean 196004
Stdev 1859.56
Quantile 0.025 192216
Quantile 0.25 195014
Quantile 0.5 195956
Quantile 0.75 196923
Quantile 0.975 200131
Mean 273620
Stdev 2590.9
Quantile 0.025 268155
Quantile 0.25 272270
Quantile 0.5 273598
Quantile 0.75 274934
Quantile 0.975 279185
Mean 271463
Stdev 2570.22
Quantile 0.025 266107
Quantile 0.25 270114
Quantile 0.5 271426
Quantile 0.75 272756
Quantile 0.975 277049
Mean 474637
Stdev 4491.5
Quantile 0.025 465017
Quantile 0.25 472321
Quantile 0.5 474635
Quantile 0.75 476942
Quantile 0.975 484141
Mean 616710
Stdev 5835.16
Quantile 0.025 604049
Quantile 0.25 613727
Quantile 0.5 616746
Quantile 0.75 619732
Quantile 0.975 628895
Mean 339066
Stdev 3209.68
Quantile 0.025 332357
Quantile 0.25 337383
Quantile 0.5 339024
Quantile 0.75 340684
Quantile 0.975 346021
Mean 308379
Stdev 2916.22
Quantile 0.025 302164
Quantile 0.25 306870
Quantile 0.5 308370
Quantile 0.75 309871
Quantile 0.975 314579
Mean 667491
Stdev 6333.76
Quantile 0.025 653294
Quantile 0.25 664331
Quantile 0.5 667640
Quantile 0.75 670844
Quantile 0.975 680273
Mean 367678
Stdev 3477
Quantile 0.025 360271
Quantile 0.25 365877
Quantile 0.5 367666
Quantile 0.75 369456
Quantile 0.975 375073
Mean 286826
Stdev 2714.16
Quantile 0.025 281109
Quantile 0.25 285410
Quantile 0.5 286801
Quantile 0.75 288202
Quantile 0.975 292663
Mean 294020
Stdev 2787.75
Quantile 0.025 288289
Quantile 0.25 292545
Quantile 0.5 293961
Quantile 0.75 295408
Quantile 0.975 300156
Mean 208912
Stdev 1976.72
Quantile 0.025 204739
Quantile 0.25 207883
Quantile 0.5 208897
Quantile 0.75 209916
Quantile 0.975 213154
Mean 216234
Stdev 2046.65
Quantile 0.025 211945
Quantile 0.25 215163
Quantile 0.5 216210
Quantile 0.75 217268
Quantile 0.975 220658
Mean 259961
Stdev 2463.26
Quantile 0.025 254979
Quantile 0.25 258643
Quantile 0.5 259889
Quantile 0.75 261175
Quantile 0.975 265462
Mean 216173
Stdev 2045.66
Quantile 0.025 211795
Quantile 0.25 215118
Quantile 0.5 216172
Quantile 0.75 217222
Quantile 0.975 220505
Mean 365159
Stdev 3457.48
Quantile 0.025 357916
Quantile 0.25 363350
Quantile 0.5 365118
Quantile 0.75 366905
Quantile 0.975 372635
Mean 199620
Stdev 1890.34
Quantile 0.025 195641
Quantile 0.25 198634
Quantile 0.5 199602
Quantile 0.75 200577
Quantile 0.975 203689
Mean 584277
Stdev 5560.44
Quantile 0.025 571553
Quantile 0.25 581550
Quantile 0.5 584472
Quantile 0.75 587263
Quantile 0.975 595244
Mean 304222
Stdev 2880.67
Quantile 0.025 298145
Quantile 0.25 302722
Quantile 0.5 304198
Quantile 0.75 305683
Quantile 0.975 310410
Mean 211627
Stdev 2002.09
Quantile 0.025 207421
Quantile 0.25 210580
Quantile 0.5 211606
Quantile 0.75 212640
Quantile 0.975 215943
Mean 227163
Stdev 2148.91
Quantile 0.025 222550
Quantile 0.25 226056
Quantile 0.5 227164
Quantile 0.75 228267
Quantile 0.975 231699
Mean 355774
Stdev 3370.35
Quantile 0.025 348586
Quantile 0.25 354032
Quantile 0.5 355765
Quantile 0.75 357496
Quantile 0.975 362938
Mean 586735
Stdev 5551.2
Quantile 0.025 574715
Quantile 0.25 583893
Quantile 0.5 586764
Quantile 0.75 589606
Quantile 0.975 598351
Mean 259919
Stdev 2465.35
Quantile 0.025 254870
Quantile 0.25 258611
Quantile 0.5 259862
Quantile 0.75 261143
Quantile 0.975 265364
Mean 280157
Stdev 2660.54
Quantile 0.025 274749
Quantile 0.25 278739
Quantile 0.5 280085
Quantile 0.75 281469
Quantile 0.975 286075
Mean 317954
Stdev 3006.69
Quantile 0.025 311510
Quantile 0.25 316404
Quantile 0.5 317954
Quantile 0.75 319498
Quantile 0.975 324311
Mean 317323
Stdev 3005.5
Quantile 0.025 310684
Quantile 0.25 315806
Quantile 0.5 317370
Quantile 0.75 318899
Quantile 0.975 323484
Mean 244833
Stdev 2319.8
Quantile 0.025 240113
Quantile 0.25 243597
Quantile 0.5 244772
Quantile 0.75 245980
Quantile 0.975 249986
Mean 359860
Stdev 3411.73
Quantile 0.025 352866
Quantile 0.25 358051
Quantile 0.5 359783
Quantile 0.75 361556
Quantile 0.975 367389
Mean 416833
Stdev 3945.92
Quantile 0.025 408364
Quantile 0.25 414801
Quantile 0.5 416835
Quantile 0.75 418860
Quantile 0.975 425166
Mean 352984
Stdev 3340.45
Quantile 0.025 345875
Quantile 0.25 351253
Quantile 0.5 352971
Quantile 0.75 354689
Quantile 0.975 360097
Mean 252876
Stdev 2391.3
Quantile 0.025 247769
Quantile 0.25 251640
Quantile 0.5 252871
Quantile 0.75 254101
Quantile 0.975 257949
Mean 255868
Stdev 2421.28
Quantile 0.025 250684
Quantile 0.25 254618
Quantile 0.5 255866
Quantile 0.75 257109
Quantile 0.975 260993
Mean 251438
Stdev 2385.02
Quantile 0.025 246586
Quantile 0.25 250167
Quantile 0.5 251374
Quantile 0.75 252616
Quantile 0.975 256738
Mean 173339
Stdev 1648.13
Quantile 0.025 170051
Quantile 0.25 172451
Quantile 0.5 173279
Quantile 0.75 174141
Quantile 0.975 177066
Mean 340465
Stdev 3219.58
Quantile 0.025 333586
Quantile 0.25 338801
Quantile 0.5 340460
Quantile 0.75 342115
Quantile 0.975 347292
Mean 361510
Stdev 3426.39
Quantile 0.025 354256
Quantile 0.25 359730
Quantile 0.5 361487
Quantile 0.75 363251
Quantile 0.975 368846
Mean 290403
Stdev 2753.41
Quantile 0.025 284719
Quantile 0.25 288950
Quantile 0.5 290350
Quantile 0.75 291778
Quantile 0.975 296440
Mean 244432
Stdev 2314.14
Quantile 0.025 239573
Quantile 0.25 243223
Quantile 0.5 244408
Quantile 0.75 245603
Quantile 0.975 249425
Mean 263025
Stdev 2489.85
Quantile 0.025 257782
Quantile 0.25 261726
Quantile 0.5 263002
Quantile 0.75 264287
Quantile 0.975 268382
Mean 524576
Stdev 4966.87
Quantile 0.025 513559
Quantile 0.25 522077
Quantile 0.5 524666
Quantile 0.75 527190
Quantile 0.975 534711
Mean 347796
Stdev 3294.83
Quantile 0.025 340952
Quantile 0.25 346063
Quantile 0.5 347743
Quantile 0.75 349449
Quantile 0.975 354979
Mean 405851
Stdev 3839.36
Quantile 0.025 397484
Quantile 0.25 403893
Quantile 0.5 405883
Quantile 0.75 407846
Quantile 0.975 413832
Mean 360089
Stdev 3414.9
Quantile 0.025 353130
Quantile 0.25 358271
Quantile 0.5 360001
Quantile 0.75 361778
Quantile 0.975 367665
Mean 345708
Stdev 3271.96
Quantile 0.025 338782
Quantile 0.25 344008
Quantile 0.5 345687
Quantile 0.75 347373
Quantile 0.975 352712
Mean 287342
Stdev 2720.5
Quantile 0.025 281635
Quantile 0.25 285919
Quantile 0.5 287311
Quantile 0.75 288716
Quantile 0.975 293216
Mean 337327
Stdev 3195.38
Quantile 0.025 330742
Quantile 0.25 335638
Quantile 0.5 337263
Quantile 0.75 338922
Quantile 0.975 344343
Mean 373406
Stdev 3532.79
Quantile 0.025 365922
Quantile 0.25 371570
Quantile 0.5 373384
Quantile 0.75 375204
Quantile 0.975 380962
Mean 309294
Stdev 2926.05
Quantile 0.025 303079
Quantile 0.25 307776
Quantile 0.5 309279
Quantile 0.75 310786
Quantile 0.975 315536
Mean 444031
Stdev 4202.99
Quantile 0.025 435163
Quantile 0.25 441841
Quantile 0.5 443996
Quantile 0.75 446164
Quantile 0.975 453057
Mean 632901
Stdev 5990.56
Quantile 0.025 619896
Quantile 0.25 629840
Quantile 0.5 632940
Quantile 0.75 636004
Quantile 0.975 645405
Mean 334026
Stdev 3158.46
Quantile 0.025 327367
Quantile 0.25 332379
Quantile 0.5 333999
Quantile 0.75 335629
Quantile 0.975 340812
Mean 353090
Stdev 3339.16
Quantile 0.025 345993
Quantile 0.25 351358
Quantile 0.5 353075
Quantile 0.75 354794
Quantile 0.975 360208
Mean 548026
Stdev 5187.03
Quantile 0.025 537062
Quantile 0.25 545327
Quantile 0.5 547987
Quantile 0.75 550661
Quantile 0.975 559145
Mean 329781
Stdev 3120.84
Quantile 0.025 323135
Quantile 0.25 328166
Quantile 0.5 329771
Quantile 0.75 331376
Quantile 0.975 336422
Mean 420882
Stdev 3980.63
Quantile 0.025 412262
Quantile 0.25 418843
Quantile 0.5 420902
Quantile 0.75 422941
Quantile 0.975 429211
Mean 326097
Stdev 3084
Quantile 0.025 319553
Quantile 0.25 324496
Quantile 0.5 326081
Quantile 0.75 327669
Quantile 0.975 332682
Mean 297246
Stdev 2813.38
Quantile 0.025 291349
Quantile 0.25 295774
Quantile 0.5 297214
Quantile 0.75 298667
Quantile 0.975 303326
Mean 351084
Stdev 3321.29
Quantile 0.025 344015
Quantile 0.25 349363
Quantile 0.5 351071
Quantile 0.75 352780
Quantile 0.975 358155
Mean 217280
Stdev 2055.42
Quantile 0.025 212891
Quantile 0.25 216217
Quantile 0.5 217276
Quantile 0.75 218332
Quantile 0.975 221642
Mean 249268
Stdev 2357.17
Quantile 0.025 244222
Quantile 0.25 248052
Quantile 0.5 249267
Quantile 0.75 250478
Quantile 0.975 254258
Mean 229436
Stdev 2172.38
Quantile 0.025 224884
Quantile 0.25 228300
Quantile 0.5 229411
Quantile 0.75 230533
Quantile 0.975 234132
Mean 223875
Stdev 2117.79
Quantile 0.025 219346
Quantile 0.25 222781
Quantile 0.5 223872
Quantile 0.75 224960
Quantile 0.975 228362
Mean 371306
Stdev 3517.92
Quantile 0.025 363854
Quantile 0.25 369480
Quantile 0.5 371284
Quantile 0.75 373095
Quantile 0.975 378833
Mean 223755
Stdev 2117.91
Quantile 0.025 219346
Quantile 0.25 222642
Quantile 0.5 223723
Quantile 0.75 224820
Quantile 0.975 228362
Mean 384422
Stdev 3635.42
Quantile 0.025 376447
Quantile 0.25 382577
Quantile 0.5 384466
Quantile 0.75 386321
Quantile 0.975 391926
Mean 466530
Stdev 4413.34
Quantile 0.025 456915
Quantile 0.25 464279
Quantile 0.5 466567
Quantile 0.75 468823
Quantile 0.975 475707
Mean 255724
Stdev 2426.07
Quantile 0.025 250765
Quantile 0.25 254435
Quantile 0.5 255665
Quantile 0.75 256926
Quantile 0.975 261092
Mean 366744
Stdev 3471.95
Quantile 0.025 359447
Quantile 0.25 364931
Quantile 0.5 366709
Quantile 0.75 368501
Quantile 0.975 374227
Mean 347815
Stdev 3293.21
Quantile 0.025 340853
Quantile 0.25 346102
Quantile 0.5 347791
Quantile 0.75 349488
Quantile 0.975 354874
Mean 264938
Stdev 2509.28
Quantile 0.025 259675
Quantile 0.25 263627
Quantile 0.5 264910
Quantile 0.75 266206
Quantile 0.975 270358
Mean 196718
Stdev 1861.49
Quantile 0.025 192797
Quantile 0.25 195747
Quantile 0.5 196701
Quantile 0.75 197661
Quantile 0.975 200721
Mean 202679
Stdev 1915.94
Quantile 0.025 198585
Quantile 0.25 201689
Quantile 0.5 202676
Quantile 0.75 203661
Quantile 0.975 206741
Mean 235089
Stdev 2224.57
Quantile 0.025 230505
Quantile 0.25 233912
Quantile 0.5 235044
Quantile 0.75 236200
Quantile 0.975 239973
Mean 278044
Stdev 2637.59
Quantile 0.025 272665
Quantile 0.25 276641
Quantile 0.5 277977
Quantile 0.75 279349
Quantile 0.975 283893
Mean 489241
Stdev 4629.47
Quantile 0.025 479484
Quantile 0.25 486827
Quantile 0.5 489200
Quantile 0.75 491589
Quantile 0.975 499193
Mean 352292
Stdev 3332.12
Quantile 0.025 345063
Quantile 0.25 350588
Quantile 0.5 352312
Quantile 0.75 354018
Quantile 0.975 359250
Mean 369273
Stdev 3499.11
Quantile 0.025 362112
Quantile 0.25 367415
Quantile 0.5 369191
Quantile 0.75 371010
Quantile 0.975 377006
Mean 216155
Stdev 2054.67
Quantile 0.025 212030
Quantile 0.25 215053
Quantile 0.5 216087
Quantile 0.75 217160
Quantile 0.975 220776
Mean 383573
Stdev 3629.48
Quantile 0.025 375685
Quantile 0.25 381719
Quantile 0.5 383599
Quantile 0.75 385455
Quantile 0.975 391140
Mean 337242
Stdev 3191.58
Quantile 0.025 330536
Quantile 0.25 335575
Quantile 0.5 337209
Quantile 0.75 338857
Quantile 0.975 344123
Mean 618422
Stdev 5856.28
Quantile 0.025 605882
Quantile 0.25 615402
Quantile 0.5 618417
Quantile 0.75 621424
Quantile 0.975 630818
Mean 333145
Stdev 3151.8
Quantile 0.025 326528
Quantile 0.25 331497
Quantile 0.5 333111
Quantile 0.75 334739
Quantile 0.975 339945
Mean 426599
Stdev 4037.29
Quantile 0.025 417735
Quantile 0.25 424552
Quantile 0.5 426649
Quantile 0.75 428708
Quantile 0.975 434927
Mean 165674
Stdev 1572.39
Quantile 0.025 162450
Quantile 0.25 164841
Quantile 0.5 165638
Quantile 0.75 166454
Quantile 0.975 169144
Mean 455532
Stdev 4307.68
Quantile 0.025 446295
Quantile 0.25 453311
Quantile 0.5 455533
Quantile 0.75 457745
Quantile 0.975 464635
Mean 447198
Stdev 4233.79
Quantile 0.025 438216
Quantile 0.25 445001
Quantile 0.5 447175
Quantile 0.75 449355
Quantile 0.975 456241
Mean 608121
Stdev 5801.07
Quantile 0.025 594662
Quantile 0.25 605310
Quantile 0.5 608371
Quantile 0.75 611265
Quantile 0.975 619380
Mean 226495
Stdev 2142.73
Quantile 0.025 221943
Quantile 0.25 225383
Quantile 0.5 226485
Quantile 0.75 227588
Quantile 0.975 231065
Mean 385114
Stdev 3647.59
Quantile 0.025 377398
Quantile 0.25 383218
Quantile 0.5 385088
Quantile 0.75 386967
Quantile 0.975 392928
Mean 744553
Stdev 7058.33
Quantile 0.025 728766
Quantile 0.25 741025
Quantile 0.5 744712
Quantile 0.75 748287
Quantile 0.975 758828
Mean 325693
Stdev 3080.12
Quantile 0.025 319152
Quantile 0.25 324095
Quantile 0.5 325678
Quantile 0.75 327265
Quantile 0.975 332264
Mean 296325
Stdev 2804.01
Quantile 0.025 290417
Quantile 0.25 294863
Quantile 0.5 296300
Quantile 0.75 297747
Quantile 0.975 302354
Mean 419722
Stdev 3970.53
Quantile 0.025 411184
Quantile 0.25 417679
Quantile 0.5 419728
Quantile 0.75 421765
Quantile 0.975 428089
Mean 397681
Stdev 3763.44
Quantile 0.025 389672
Quantile 0.25 395732
Quantile 0.5 397667
Quantile 0.75 399603
Quantile 0.975 405695
Mean 169366
Stdev 1615.5
Quantile 0.025 166188
Quantile 0.25 168490
Quantile 0.5 169297
Quantile 0.75 170143
Quantile 0.975 173065
Mean 280531
Stdev 2656.65
Quantile 0.025 274944
Quantile 0.25 279145
Quantile 0.5 280505
Quantile 0.75 281876
Quantile 0.975 286255
Mean 166176
Stdev 1575.09
Quantile 0.025 162950
Quantile 0.25 165340
Quantile 0.5 166140
Quantile 0.75 166958
Quantile 0.975 169655
Mean 214021
Stdev 2025.26
Quantile 0.025 209757
Quantile 0.25 212964
Quantile 0.5 214002
Quantile 0.75 215047
Quantile 0.975 218379
Mean 315900
Stdev 2990.75
Quantile 0.025 309556
Quantile 0.25 314347
Quantile 0.5 315883
Quantile 0.75 317423
Quantile 0.975 322289
Mean 426244
Stdev 4030.85
Quantile 0.025 417461
Quantile 0.25 424188
Quantile 0.5 426278
Quantile 0.75 428338
Quantile 0.975 434624
Mean 275515
Stdev 2608.73
Quantile 0.025 270006
Quantile 0.25 274158
Quantile 0.5 275495
Quantile 0.75 276840
Quantile 0.975 281112
Mean 239540
Stdev 2285.68
Quantile 0.025 235052
Quantile 0.25 238299
Quantile 0.5 239440
Quantile 0.75 240638
Quantile 0.975 244782
Mean 364863
Stdev 3453.94
Quantile 0.025 357481
Quantile 0.25 363079
Quantile 0.5 364857
Quantile 0.75 366631
Quantile 0.975 372187
Mean 145657
Stdev 1411.25
Quantile 0.025 143043
Quantile 0.25 144869
Quantile 0.5 145555
Quantile 0.75 146301
Quantile 0.975 149050
Mean 272782
Stdev 2581.79
Quantile 0.025 267430
Quantile 0.25 271421
Quantile 0.5 272738
Quantile 0.75 274076
Quantile 0.975 278419
Mean 274847
Stdev 2608.59
Quantile 0.025 269535
Quantile 0.25 273459
Quantile 0.5 274779
Quantile 0.75 276136
Quantile 0.975 280639
Mean 269246
Stdev 2547.97
Quantile 0.025 263760
Quantile 0.25 267936
Quantile 0.5 269251
Quantile 0.75 270558
Quantile 0.975 274609
Mean 251405
Stdev 2379.42
Quantile 0.025 246367
Quantile 0.25 250168
Quantile 0.5 251390
Quantile 0.75 252616
Quantile 0.975 256497
Mean 320254
Stdev 3029.5
Quantile 0.025 313759
Quantile 0.25 318692
Quantile 0.5 320253
Quantile 0.75 321809
Quantile 0.975 326657
Mean 308197
Stdev 2921.34
Quantile 0.025 302146
Quantile 0.25 306658
Quantile 0.5 308145
Quantile 0.75 309659
Quantile 0.975 314583
Mean 314212
Stdev 2973.94
Quantile 0.025 307922
Quantile 0.25 312665
Quantile 0.5 314191
Quantile 0.75 315723
Quantile 0.975 320583
Mean 243049
Stdev 2300.87
Quantile 0.025 238244
Quantile 0.25 241843
Quantile 0.5 243019
Quantile 0.75 244209
Quantile 0.975 248039
Mean 454607
Stdev 4301.46
Quantile 0.025 445196
Quantile 0.25 452421
Quantile 0.5 454653
Quantile 0.75 456849
Quantile 0.975 463512
Mean 340556
Stdev 3225.7
Quantile 0.025 333799
Quantile 0.25 338869
Quantile 0.5 340518
Quantile 0.75 342184
Quantile 0.975 347532
Mean 506676
Stdev 4795.12
Quantile 0.025 496320
Quantile 0.25 504217
Quantile 0.5 506694
Quantile 0.75 509150
Quantile 0.975 516737
Mean 154333
Stdev 1469.15
Quantile 0.025 151417
Quantile 0.25 153540
Quantile 0.5 154277
Quantile 0.75 155045
Quantile 0.975 157670
Mean 185752
Stdev 1784.13
Quantile 0.025 182342
Quantile 0.25 184770
Quantile 0.5 185650
Quantile 0.75 186589
Quantile 0.975 189937
Mean 290446
Stdev 2751.01
Quantile 0.025 284681
Quantile 0.25 289007
Quantile 0.5 290414
Quantile 0.75 291835
Quantile 0.975 296393
Mean 214432
Stdev 2030.94
Quantile 0.025 210172
Quantile 0.25 213370
Quantile 0.5 214409
Quantile 0.75 215458
Quantile 0.975 218819
Mean 176742
Stdev 1674.65
Quantile 0.025 173254
Quantile 0.25 175863
Quantile 0.5 176717
Quantile 0.75 177584
Quantile 0.975 180384
Mean 286333
Stdev 2709.71
Quantile 0.025 280636
Quantile 0.25 284918
Quantile 0.5 286306
Quantile 0.75 287705
Quantile 0.975 292172
Mean 286270
Stdev 2711.53
Quantile 0.025 280625
Quantile 0.25 284846
Quantile 0.5 286229
Quantile 0.75 287633
Quantile 0.975 292168
Mean 317949
Stdev 3010.37
Quantile 0.025 311637
Quantile 0.25 316374
Quantile 0.5 317914
Quantile 0.75 319469
Quantile 0.975 324453
Mean 257895
Stdev 2441.52
Quantile 0.025 252708
Quantile 0.25 256629
Quantile 0.5 257883
Quantile 0.75 259139
Quantile 0.975 263103
Mean 666396
Stdev 6304.52
Quantile 0.025 653019
Quantile 0.25 663123
Quantile 0.5 666362
Quantile 0.75 669609
Quantile 0.975 679859
Mean 238843
Stdev 2259.25
Quantile 0.025 234117
Quantile 0.25 237659
Quantile 0.5 238815
Quantile 0.75 239983
Quantile 0.975 243734
Mean 252485
Stdev 2393.64
Quantile 0.025 247537
Quantile 0.25 251223
Quantile 0.5 252441
Quantile 0.75 253682
Quantile 0.975 257727
Mean 720955
Stdev 6828.67
Quantile 0.025 705806
Quantile 0.25 717519
Quantile 0.5 721078
Quantile 0.75 724547
Quantile 0.975 734888
Mean 393394
Stdev 3719.09
Quantile 0.025 385498
Quantile 0.25 391463
Quantile 0.5 393375
Quantile 0.75 395291
Quantile 0.975 401330
Mean 334783
Stdev 3168.19
Quantile 0.025 328038
Quantile 0.25 333142
Quantile 0.5 334771
Quantile 0.75 336401
Quantile 0.975 341527
Mean 244097
Stdev 2308.48
Quantile 0.025 239197
Quantile 0.25 242899
Quantile 0.5 244085
Quantile 0.75 245274
Quantile 0.975 249025
Mean 266509
Stdev 2526.89
Quantile 0.025 261313
Quantile 0.25 265171
Quantile 0.5 266455
Quantile 0.75 267767
Quantile 0.975 272070
Mean 372669
Stdev 3532.35
Quantile 0.025 364830
Quantile 0.25 370893
Quantile 0.5 372733
Quantile 0.75 374526
Quantile 0.975 379875
Mean 288136
Stdev 2728.78
Quantile 0.025 282402
Quantile 0.25 286711
Quantile 0.5 288108
Quantile 0.75 289516
Quantile 0.975 294020
Mean 230440
Stdev 2182.8
Quantile 0.025 225872
Quantile 0.25 229298
Quantile 0.5 230413
Quantile 0.75 231541
Quantile 0.975 235165
Mean 404852
Stdev 3825.86
Quantile 0.025 396517
Quantile 0.25 402900
Quantile 0.5 404884
Quantile 0.75 406841
Quantile 0.975 412805
Mean 271444
Stdev 2569.25
Quantile 0.025 266062
Quantile 0.25 270099
Quantile 0.5 271414
Quantile 0.75 272741
Quantile 0.975 276999
Mean 251802
Stdev 2388.25
Quantile 0.025 246890
Quantile 0.25 250539
Quantile 0.5 251752
Quantile 0.75 252991
Quantile 0.975 257057
Mean 465925
Stdev 4410.04
Quantile 0.025 456609
Quantile 0.25 463629
Quantile 0.5 465891
Quantile 0.75 468165
Quantile 0.975 475384
Mean 575296
Stdev 5469.97
Quantile 0.025 562795
Quantile 0.25 572609
Quantile 0.5 575484
Quantile 0.75 578232
Quantile 0.975 586098
Mean 292977
Stdev 2773.06
Quantile 0.025 286911
Quantile 0.25 291567
Quantile 0.5 293006
Quantile 0.75 294421
Quantile 0.975 298719
Mean 252671
Stdev 2393.78
Quantile 0.025 247702
Quantile 0.25 251412
Quantile 0.5 252632
Quantile 0.75 253872
Quantile 0.975 257893
Mean 336722
Stdev 3186.09
Quantile 0.025 329998
Quantile 0.25 335062
Quantile 0.5 336696
Quantile 0.75 338340
Quantile 0.975 343562
Mean 278854
Stdev 2640.66
Quantile 0.025 273335
Quantile 0.25 277470
Quantile 0.5 278820
Quantile 0.75 280185
Quantile 0.975 284577
Mean 390875
Stdev 3700.6
Quantile 0.025 383290
Quantile 0.25 388911
Quantile 0.5 390791
Quantile 0.75 392715
Quantile 0.975 399039
Mean 509427
Stdev 4819.03
Quantile 0.025 499097
Quantile 0.25 506943
Quantile 0.5 509427
Quantile 0.75 511902
Quantile 0.975 519614
Mean 390039
Stdev 3693.53
Quantile 0.025 382262
Quantile 0.25 388112
Quantile 0.5 390004
Quantile 0.75 391909
Quantile 0.975 397987
Mean 239631
Stdev 2267.07
Quantile 0.025 234871
Quantile 0.25 238446
Quantile 0.5 239607
Quantile 0.75 240779
Quantile 0.975 244522
Mean 267025
Stdev 2526.79
Quantile 0.025 261703
Quantile 0.25 265707
Quantile 0.5 267002
Quantile 0.75 268306
Quantile 0.975 272460
Mean 236827
Stdev 2246.97
Quantile 0.025 232251
Quantile 0.25 235630
Quantile 0.5 236768
Quantile 0.75 237937
Quantile 0.975 241816
Mean 356658
Stdev 3374.6
Quantile 0.025 349589
Quantile 0.25 354892
Quantile 0.5 356618
Quantile 0.75 358363
Quantile 0.975 363954
Mean 216414
Stdev 2081.31
Quantile 0.025 212466
Quantile 0.25 215265
Quantile 0.5 216288
Quantile 0.75 217385
Quantile 0.975 221325
Mean 323807
Stdev 3088.27
Quantile 0.025 317716
Quantile 0.25 322134
Quantile 0.5 323678
Quantile 0.75 325295
Quantile 0.975 330863
Mean 543397
Stdev 5156.07
Quantile 0.025 532906
Quantile 0.25 540651
Quantile 0.5 543261
Quantile 0.75 545944
Quantile 0.975 554854
Mean 329117
Stdev 3112.57
Quantile 0.025 322391
Quantile 0.25 327520
Quantile 0.5 329129
Quantile 0.75 330724
Quantile 0.975 335643
Mean 388702
Stdev 3681.89
Quantile 0.025 380597
Quantile 0.25 386840
Quantile 0.5 388753
Quantile 0.75 390628
Quantile 0.975 396277
Mean 328754
Stdev 3107.72
Quantile 0.025 322094
Quantile 0.25 327150
Quantile 0.5 328753
Quantile 0.75 330350
Quantile 0.975 335324
Mean 642787
Stdev 6097
Quantile 0.025 629089
Quantile 0.25 639750
Quantile 0.5 642939
Quantile 0.75 646022
Quantile 0.975 655059
Mean 276675
Stdev 2618.24
Quantile 0.025 271236
Quantile 0.25 275297
Quantile 0.5 276633
Quantile 0.75 277990
Quantile 0.975 282381
Mean 301608
Stdev 2853.71
Quantile 0.025 295419
Quantile 0.25 300149
Quantile 0.5 301626
Quantile 0.75 303086
Quantile 0.975 307570
Mean 354425
Stdev 3352.47
Quantile 0.025 347353
Quantile 0.25 352678
Quantile 0.5 354397
Quantile 0.75 356127
Quantile 0.975 361624
Mean 438327
Stdev 4151.35
Quantile 0.025 429715
Quantile 0.25 436142
Quantile 0.5 438258
Quantile 0.75 440409
Quantile 0.975 447387
Mean 726768
Stdev 6876.69
Quantile 0.025 711835
Quantile 0.25 723254
Quantile 0.5 726814
Quantile 0.75 730331
Quantile 0.975 741116
Mean 319943
Stdev 3025.54
Quantile 0.025 313441
Quantile 0.25 318385
Quantile 0.5 319947
Quantile 0.75 321500
Quantile 0.975 326322
Mean 276057
Stdev 2612.49
Quantile 0.025 270604
Quantile 0.25 274687
Quantile 0.5 276022
Quantile 0.75 277374
Quantile 0.975 281724
Mean 184584
Stdev 1804.43
Quantile 0.025 181322
Quantile 0.25 183568
Quantile 0.5 184434
Quantile 0.75 185389
Quantile 0.975 189000
Mean 312155
Stdev 2961.69
Quantile 0.025 306106
Quantile 0.25 310581
Quantile 0.5 312082
Quantile 0.75 313622
Quantile 0.975 318713
Mean 280938
Stdev 2662.63
Quantile 0.025 275500
Quantile 0.25 279523
Quantile 0.5 280873
Quantile 0.75 282258
Quantile 0.975 286833
Mean 243413
Stdev 2300.68
Quantile 0.025 238553
Quantile 0.25 242214
Quantile 0.5 243395
Quantile 0.75 244582
Quantile 0.975 248346
Mean 319581
Stdev 3021.11
Quantile 0.025 313147
Quantile 0.25 318016
Quantile 0.5 319571
Quantile 0.75 321126
Quantile 0.975 326008
Mean 286141
Stdev 2702.45
Quantile 0.025 280473
Quantile 0.25 284726
Quantile 0.5 286111
Quantile 0.75 287509
Quantile 0.975 291975
Mean 365009
Stdev 3450.97
Quantile 0.025 357704
Quantile 0.25 363214
Quantile 0.5 364986
Quantile 0.75 366766
Quantile 0.975 372394
Mean 279503
Stdev 2657.12
Quantile 0.025 274173
Quantile 0.25 278077
Quantile 0.5 279415
Quantile 0.75 280802
Quantile 0.975 285484
Mean 416928
Stdev 3940.87
Quantile 0.025 408615
Quantile 0.25 414874
Quantile 0.5 416896
Quantile 0.75 418930
Quantile 0.975 425389
Mean 287631
Stdev 2722.9
Quantile 0.025 281904
Quantile 0.25 286210
Quantile 0.5 287605
Quantile 0.75 289010
Quantile 0.975 293496
Mean 285622
Stdev 2703.63
Quantile 0.025 279922
Quantile 0.25 284213
Quantile 0.5 285599
Quantile 0.75 286994
Quantile 0.975 291432
Mean 619681
Stdev 5880.06
Quantile 0.025 606434
Quantile 0.25 616759
Quantile 0.5 619836
Quantile 0.75 622807
Quantile 0.975 631480
Mean 336563
Stdev 3185.9
Quantile 0.025 329900
Quantile 0.25 334893
Quantile 0.5 336522
Quantile 0.75 338169
Quantile 0.975 343462
Mean 289047
Stdev 2736.81
Quantile 0.025 283312
Quantile 0.25 287615
Quantile 0.5 289014
Quantile 0.75 290428
Quantile 0.975 294963
Mean 337166
Stdev 3192.9
Quantile 0.025 330495
Quantile 0.25 335493
Quantile 0.5 337124
Quantile 0.75 338775
Quantile 0.975 344087
Mean 256865
Stdev 2431.4
Quantile 0.025 251807
Quantile 0.25 255587
Quantile 0.5 256828
Quantile 0.75 258087
Quantile 0.975 262157
Mean 482641
Stdev 4562.22
Quantile 0.025 473029
Quantile 0.25 480261
Quantile 0.5 482601
Quantile 0.75 484957
Quantile 0.975 492449
Mean 378118
Stdev 3578.9
Quantile 0.025 370555
Quantile 0.25 376256
Quantile 0.5 378091
Quantile 0.75 379936
Quantile 0.975 385792
Mean 390976
Stdev 3714.57
Quantile 0.025 383511
Quantile 0.25 388983
Quantile 0.5 390855
Quantile 0.75 392794
Quantile 0.975 399323
Mean 795361
Stdev 7539.39
Quantile 0.025 778561
Quantile 0.25 791581
Quantile 0.5 795514
Quantile 0.75 799338
Quantile 0.975 810672
Mean 538295
Stdev 5102.17
Quantile 0.025 527767
Quantile 0.25 535601
Quantile 0.5 538196
Quantile 0.75 540842
Quantile 0.975 549487
Mean 305961
Stdev 2901.63
Quantile 0.025 300049
Quantile 0.25 304417
Quantile 0.5 305886
Quantile 0.75 307396
Quantile 0.975 312400
Mean 261883
Stdev 2478.27
Quantile 0.025 256601
Quantile 0.25 260600
Quantile 0.5 261875
Quantile 0.75 263150
Quantile 0.975 267153
Mean 297794
Stdev 2818.27
Quantile 0.025 291809
Quantile 0.25 296333
Quantile 0.5 297781
Quantile 0.75 299231
Quantile 0.975 303808
Mean 291947
Stdev 2764.26
Quantile 0.025 286155
Quantile 0.25 290501
Quantile 0.5 291914
Quantile 0.75 293342
Quantile 0.975 297923
Mean 244524
Stdev 2319.45
Quantile 0.025 239791
Quantile 0.25 243291
Quantile 0.5 244466
Quantile 0.75 245672
Quantile 0.975 249665
Mean 282671
Stdev 2676.63
Quantile 0.025 277103
Quantile 0.25 281265
Quantile 0.5 282630
Quantile 0.75 284016
Quantile 0.975 288497
Mean 428634
Stdev 4054.5
Quantile 0.025 420088
Quantile 0.25 426520
Quantile 0.5 428599
Quantile 0.75 430692
Quantile 0.975 437347
Mean 314823
Stdev 2978.94
Quantile 0.025 308540
Quantile 0.25 313270
Quantile 0.5 314798
Quantile 0.75 316335
Quantile 0.975 321221
Mean 260082
Stdev 2461.22
Quantile 0.025 254835
Quantile 0.25 258809
Quantile 0.5 260075
Quantile 0.75 261341
Quantile 0.975 265314
Mean 303166
Stdev 2870.2
Quantile 0.025 297179
Quantile 0.25 301660
Quantile 0.5 303126
Quantile 0.75 304611
Quantile 0.975 309398
Mean 258608
Stdev 2448.52
Quantile 0.025 253428
Quantile 0.25 257335
Quantile 0.5 258592
Quantile 0.75 259853
Quantile 0.975 263853
Mean 227075
Stdev 2146.56
Quantile 0.025 222487
Quantile 0.25 225966
Quantile 0.5 227072
Quantile 0.75 228176
Quantile 0.975 231625
Mean 242040
Stdev 2291.78
Quantile 0.025 237241
Quantile 0.25 240841
Quantile 0.5 242013
Quantile 0.75 243197
Quantile 0.975 246997
Mean 325003
Stdev 3078.55
Quantile 0.025 318630
Quantile 0.25 323380
Quantile 0.5 324949
Quantile 0.75 326544
Quantile 0.975 331734
Mean 297588
Stdev 2817.22
Quantile 0.025 291594
Quantile 0.25 296128
Quantile 0.5 297576
Quantile 0.75 299026
Quantile 0.975 303589
Mean 322723
Stdev 3052.03
Quantile 0.025 316135
Quantile 0.25 321157
Quantile 0.5 322734
Quantile 0.75 324298
Quantile 0.975 329129
Mean 358388
Stdev 3390.45
Quantile 0.025 351180
Quantile 0.25 356630
Quantile 0.5 358373
Quantile 0.75 360119
Quantile 0.975 365614
Mean 313840
Stdev 2969.09
Quantile 0.025 307604
Quantile 0.25 312288
Quantile 0.5 313809
Quantile 0.75 315343
Quantile 0.975 320243
Mean 348598
Stdev 3295.91
Quantile 0.025 341455
Quantile 0.25 346910
Quantile 0.5 348616
Quantile 0.75 350304
Quantile 0.975 355488
Mean 330524
Stdev 3123.09
Quantile 0.025 323937
Quantile 0.25 328895
Quantile 0.5 330498
Quantile 0.75 332110
Quantile 0.975 337230
Mean 214761
Stdev 2033.91
Quantile 0.025 210539
Quantile 0.25 213690
Quantile 0.5 214728
Quantile 0.75 215781
Quantile 0.975 219197
Mean 387146
Stdev 3663.57
Quantile 0.025 379294
Quantile 0.25 385257
Quantile 0.5 387145
Quantile 0.75 389026
Quantile 0.975 394893
Mean 287574
Stdev 2721.35
Quantile 0.025 281763
Quantile 0.25 286167
Quantile 0.5 287568
Quantile 0.75 288967
Quantile 0.975 293350
Mean 337276
Stdev 3191.73
Quantile 0.025 330472
Quantile 0.25 335625
Quantile 0.5 337267
Quantile 0.75 338908
Quantile 0.975 344061
Mean 280154
Stdev 2647.4
Quantile 0.025 274471
Quantile 0.25 278789
Quantile 0.5 280156
Quantile 0.75 281516
Quantile 0.975 285741
Mean 200307
Stdev 1895.86
Quantile 0.025 196298
Quantile 0.25 199321
Quantile 0.5 200294
Quantile 0.75 201271
Quantile 0.975 204369
Mean 278896
Stdev 2637.47
Quantile 0.025 273148
Quantile 0.25 277551
Quantile 0.5 278919
Quantile 0.75 280267
Quantile 0.975 284378
Mean 261141
Stdev 2473.45
Quantile 0.025 255958
Quantile 0.25 259848
Quantile 0.5 261112
Quantile 0.75 262390
Quantile 0.975 266489
Mean 399287
Stdev 3780.04
Quantile 0.025 391251
Quantile 0.25 397328
Quantile 0.5 399271
Quantile 0.75 401216
Quantile 0.975 407345
Mean 629276
Stdev 5956.69
Quantile 0.025 616158
Quantile 0.25 626263
Quantile 0.5 629360
Quantile 0.75 632394
Quantile 0.975 641524
Mean 335499
Stdev 3180.94
Quantile 0.025 328902
Quantile 0.25 333825
Quantile 0.5 335445
Quantile 0.75 337092
Quantile 0.975 342444
Mean 400163
Stdev 3786.58
Quantile 0.025 391927
Quantile 0.25 398230
Quantile 0.5 400192
Quantile 0.75 402128
Quantile 0.975 408050
Mean 383871
Stdev 3636.26
Quantile 0.025 376265
Quantile 0.25 381967
Quantile 0.5 383825
Quantile 0.75 385704
Quantile 0.975 391746
Mean 436038
Stdev 4126.7
Quantile 0.025 426895
Quantile 0.25 433959
Quantile 0.5 436110
Quantile 0.75 438208
Quantile 0.975 444467
Mean 369963
Stdev 3501.81
Quantile 0.025 362630
Quantile 0.25 368130
Quantile 0.5 369920
Quantile 0.75 371730
Quantile 0.975 377537
Mean 567262
Stdev 5370.38
Quantile 0.025 555664
Quantile 0.25 564508
Quantile 0.5 567282
Quantile 0.75 570033
Quantile 0.975 578532
Mean 518866
Stdev 4913.5
Quantile 0.025 508092
Quantile 0.25 516373
Quantile 0.5 518923
Quantile 0.75 521428
Quantile 0.975 529017
Mean 435186
Stdev 4115.77
Quantile 0.025 426286
Quantile 0.25 433076
Quantile 0.5 435204
Quantile 0.75 437313
Quantile 0.975 443810
Mean 326775
Stdev 3099.37
Quantile 0.025 320314
Quantile 0.25 325150
Quantile 0.5 326730
Quantile 0.75 328332
Quantile 0.975 333511
Mean 229475
Stdev 2174.6
Quantile 0.025 224977
Quantile 0.25 228329
Quantile 0.5 229436
Quantile 0.75 230563
Quantile 0.975 234234
Mean 242503
Stdev 2308.44
Quantile 0.025 237911
Quantile 0.25 241258
Quantile 0.5 242416
Quantile 0.75 243623
Quantile 0.975 247737
Mean 269007
Stdev 2546.93
Quantile 0.025 263616
Quantile 0.25 267683
Quantile 0.5 268990
Quantile 0.75 270302
Quantile 0.975 274459
Mean 294448
Stdev 2792.89
Quantile 0.025 288748
Quantile 0.25 292964
Quantile 0.5 294379
Quantile 0.75 295831
Quantile 0.975 300636
Mean 236643
Stdev 2240.05
Quantile 0.025 231958
Quantile 0.25 235470
Quantile 0.5 236615
Quantile 0.75 237773
Quantile 0.975 241494
Mean 271411
Stdev 2567.95
Quantile 0.025 265981
Quantile 0.25 270075
Quantile 0.5 271392
Quantile 0.75 272716
Quantile 0.975 276913
Mean 276340
Stdev 2613.58
Quantile 0.025 270859
Quantile 0.25 274973
Quantile 0.5 276311
Quantile 0.75 277662
Quantile 0.975 281984
Mean 413870
Stdev 3917.45
Quantile 0.025 405669
Quantile 0.25 411819
Quantile 0.5 413823
Quantile 0.75 415848
Quantile 0.975 422345
Mean 468024
Stdev 4424.52
Quantile 0.025 458378
Quantile 0.25 465768
Quantile 0.5 468063
Quantile 0.75 470325
Quantile 0.975 477216
Mean 799140
Stdev 7565.22
Quantile 0.025 782853
Quantile 0.25 795253
Quantile 0.5 799156
Quantile 0.75 803035
Quantile 0.975 815067
Mean 629872
Stdev 5976.67
Quantile 0.025 616409
Quantile 0.25 626901
Quantile 0.5 630030
Quantile 0.75 633049
Quantile 0.975 641866
Mean 613385
Stdev 5803.12
Quantile 0.025 601205
Quantile 0.25 610351
Quantile 0.5 613322
Quantile 0.75 616321
Quantile 0.975 625908
Mean 174822
Stdev 1726.98
Quantile 0.025 171777
Quantile 0.25 173840
Quantile 0.5 174658
Quantile 0.75 175574
Quantile 0.975 179122
Mean 374797
Stdev 3547.07
Quantile 0.025 366971
Quantile 0.25 373005
Quantile 0.5 374851
Quantile 0.75 376657
Quantile 0.975 382075
Mean 478626
Stdev 4537.57
Quantile 0.025 468445
Quantile 0.25 476363
Quantile 0.5 478736
Quantile 0.75 481032
Quantile 0.975 487771
Mean 161315
Stdev 1533.24
Quantile 0.025 158234
Quantile 0.25 160492
Quantile 0.5 161264
Quantile 0.75 162064
Quantile 0.975 164761
Mean 286498
Stdev 2712.38
Quantile 0.025 280743
Quantile 0.25 285091
Quantile 0.5 286484
Quantile 0.75 287880
Quantile 0.975 292291
Mean 225679
Stdev 2137.41
Quantile 0.025 221265
Quantile 0.25 224550
Quantile 0.5 225638
Quantile 0.75 226747
Quantile 0.975 230363
Mean 282237
Stdev 2669.09
Quantile 0.025 276482
Quantile 0.25 280866
Quantile 0.5 282245
Quantile 0.75 283613
Quantile 0.975 287846
Mean 297032
Stdev 2813.88
Quantile 0.025 291112
Quantile 0.25 295564
Quantile 0.5 297005
Quantile 0.75 298456
Quantile 0.975 303093
Mean 445059
Stdev 4216.8
Quantile 0.025 436354
Quantile 0.25 442832
Quantile 0.5 444977
Quantile 0.75 447165
Quantile 0.975 454304
Mean 263853
Stdev 2497.82
Quantile 0.025 258636
Quantile 0.25 262544
Quantile 0.5 263820
Quantile 0.75 265112
Quantile 0.975 269270
Mean 432131
Stdev 4083.54
Quantile 0.025 423370
Quantile 0.25 430026
Quantile 0.5 432133
Quantile 0.75 434231
Quantile 0.975 440754
Mean 304379
Stdev 2878.71
Quantile 0.025 298093
Quantile 0.25 302913
Quantile 0.5 304407
Quantile 0.75 305877
Quantile 0.975 310350
Mean 288772
Stdev 2742.33
Quantile 0.025 283214
Quantile 0.25 287308
Quantile 0.5 288694
Quantile 0.75 290122
Quantile 0.975 294888
Mean 251402
Stdev 2381.9
Quantile 0.025 246503
Quantile 0.25 250141
Quantile 0.5 251351
Quantile 0.75 252588
Quantile 0.975 256642
Mean 308424
Stdev 2917.4
Quantile 0.025 302273
Quantile 0.25 306903
Quantile 0.5 308399
Quantile 0.75 309904
Quantile 0.975 314692
Mean 387231
Stdev 3661.85
Quantile 0.025 379362
Quantile 0.25 385345
Quantile 0.5 387235
Quantile 0.75 389115
Quantile 0.975 394952
Mean 473315
Stdev 4481.59
Quantile 0.025 463984
Quantile 0.25 470960
Quantile 0.5 473248
Quantile 0.75 475568
Quantile 0.975 483061
Mean 229043
Stdev 2174.99
Quantile 0.025 224645
Quantile 0.25 227881
Quantile 0.5 228979
Quantile 0.75 230112
Quantile 0.975 233903
Mean 229948
Stdev 2176.89
Quantile 0.025 225403
Quantile 0.25 228806
Quantile 0.5 229918
Quantile 0.75 231044
Quantile 0.975 234670
Mean 219011
Stdev 2071.51
Quantile 0.025 214636
Quantile 0.25 217933
Quantile 0.5 218996
Quantile 0.75 220064
Quantile 0.975 223454
Mean 198381
Stdev 1875.98
Quantile 0.025 194374
Quantile 0.25 197411
Quantile 0.5 198377
Quantile 0.75 199342
Quantile 0.975 202361
Mean 387753
Stdev 3669.74
Quantile 0.025 380049
Quantile 0.25 385834
Quantile 0.5 387713
Quantile 0.75 389608
Quantile 0.975 395671
Mean 419156
Stdev 3969.3
Quantile 0.025 410670
Quantile 0.25 417107
Quantile 0.5 419150
Quantile 0.75 421188
Quantile 0.975 427572
Mean 376523
Stdev 3563.93
Quantile 0.025 369000
Quantile 0.25 374668
Quantile 0.5 376495
Quantile 0.75 378333
Quantile 0.975 384173
Mean 445880
Stdev 4216.96
Quantile 0.025 436758
Quantile 0.25 443719
Quantile 0.5 445900
Quantile 0.75 448060
Quantile 0.975 454712
Mean 319938
Stdev 3028.38
Quantile 0.025 313272
Quantile 0.25 318405
Quantile 0.5 319980
Quantile 0.75 321522
Quantile 0.975 326168
Mean 285549
Stdev 2702.21
Quantile 0.025 279593
Quantile 0.25 284183
Quantile 0.5 285589
Quantile 0.75 286965
Quantile 0.975 291100
Mean 466731
Stdev 4418.32
Quantile 0.025 457106
Quantile 0.25 464479
Quantile 0.5 466767
Quantile 0.75 469025
Quantile 0.975 475920
Mean 392826
Stdev 3721.03
Quantile 0.025 385123
Quantile 0.25 390864
Quantile 0.5 392759
Quantile 0.75 394688
Quantile 0.975 400963
Mean 304997
Stdev 2886.47
Quantile 0.025 298871
Quantile 0.25 303499
Quantile 0.5 304982
Quantile 0.75 306468
Quantile 0.975 311160
Mean 550825
Stdev 5213.55
Quantile 0.025 539807
Quantile 0.25 548113
Quantile 0.5 550787
Quantile 0.75 553475
Quantile 0.975 562003
Mean 519218
Stdev 4911.54
Quantile 0.025 508530
Quantile 0.25 516712
Quantile 0.5 519257
Quantile 0.75 521768
Quantile 0.975 529443
Mean 415667
Stdev 3931.67
Quantile 0.025 407130
Quantile 0.25 413658
Quantile 0.5 415693
Quantile 0.75 417705
Quantile 0.975 423870
Mean 338528
Stdev 3205.61
Quantile 0.025 331772
Quantile 0.25 336858
Quantile 0.5 338500
Quantile 0.75 340153
Quantile 0.975 345420
Mean 341038
Stdev 3227.58
Quantile 0.025 333951
Quantile 0.25 339402
Quantile 0.5 341079
Quantile 0.75 342724
Quantile 0.975 347695
Mean 364073
Stdev 3450.04
Quantile 0.025 357016
Quantile 0.25 362240
Quantile 0.5 363991
Quantile 0.75 365785
Quantile 0.975 371700
Mean 458859
Stdev 4340.72
Quantile 0.025 449293
Quantile 0.25 456663
Quantile 0.5 458922
Quantile 0.75 461133
Quantile 0.975 467776
Mean 617648
Stdev 5846.48
Quantile 0.025 605320
Quantile 0.25 614601
Quantile 0.5 617598
Quantile 0.75 620613
Quantile 0.975 630210
Mean 449221
Stdev 4246.56
Quantile 0.025 440098
Quantile 0.25 447034
Quantile 0.5 449226
Quantile 0.75 451406
Quantile 0.975 458177
Mean 326659
Stdev 3091.98
Quantile 0.025 319891
Quantile 0.25 325088
Quantile 0.5 326693
Quantile 0.75 328270
Quantile 0.975 333058
Mean 235577
Stdev 2240.1
Quantile 0.025 231090
Quantile 0.25 234373
Quantile 0.5 235500
Quantile 0.75 236669
Quantile 0.975 240626
Mean 248409
Stdev 2350.3
Quantile 0.025 243438
Quantile 0.25 247186
Quantile 0.5 248393
Quantile 0.75 249604
Quantile 0.975 253444
Mean 291430
Stdev 2757.81
Quantile 0.025 285327
Quantile 0.25 290039
Quantile 0.5 291476
Quantile 0.75 292879
Quantile 0.975 297070
Mean 362171
Stdev 3423.67
Quantile 0.025 354868
Quantile 0.25 360399
Quantile 0.5 362162
Quantile 0.75 363924
Quantile 0.975 369443
Mean 187627
Stdev 1776.44
Quantile 0.025 183901
Quantile 0.25 186699
Quantile 0.5 187608
Quantile 0.75 188525
Quantile 0.975 191464
Mean 453438
Stdev 4292.2
Quantile 0.025 444392
Quantile 0.25 451201
Quantile 0.5 453400
Quantile 0.75 455614
Quantile 0.975 462665
Mean 199934
Stdev 1892.48
Quantile 0.025 195973
Quantile 0.25 198944
Quantile 0.5 199911
Quantile 0.75 200890
Quantile 0.975 204029
Mean 321577
Stdev 3041.58
Quantile 0.025 315243
Quantile 0.25 319978
Quantile 0.5 321532
Quantile 0.75 323108
Quantile 0.975 328189
Mean 200011
Stdev 1891.8
Quantile 0.025 196015
Quantile 0.25 199026
Quantile 0.5 199996
Quantile 0.75 200972
Quantile 0.975 204069
Mean 230410
Stdev 2180.06
Quantile 0.025 225803
Quantile 0.25 229276
Quantile 0.5 230394
Quantile 0.75 231518
Quantile 0.975 235084
Mean 271821
Stdev 2573.9
Quantile 0.025 266394
Quantile 0.25 270480
Quantile 0.5 271799
Quantile 0.75 273126
Quantile 0.975 277352
Mean 179467
Stdev 1699.99
Quantile 0.025 175963
Quantile 0.25 178568
Quantile 0.5 179433
Quantile 0.75 180315
Quantile 0.975 183199
Mean 168348
Stdev 1602.26
Quantile 0.025 165170
Quantile 0.25 167482
Quantile 0.5 168285
Quantile 0.75 169124
Quantile 0.975 171990
Mean 328834
Stdev 3110.7
Quantile 0.025 322289
Quantile 0.25 327210
Quantile 0.5 328804
Quantile 0.75 330410
Quantile 0.975 335530
Mean 250636
Stdev 2371.19
Quantile 0.025 245513
Quantile 0.25 249421
Quantile 0.5 250646
Quantile 0.75 251861
Quantile 0.975 255609
Mean 234612
Stdev 2222.99
Quantile 0.025 229915
Quantile 0.25 233456
Quantile 0.5 234595
Quantile 0.75 235740
Quantile 0.975 239381
Mean 429376
Stdev 4071.12
Quantile 0.025 420258
Quantile 0.25 427343
Quantile 0.5 429471
Quantile 0.75 431532
Quantile 0.975 437598
Mean 518654
Stdev 4907.08
Quantile 0.025 508028
Quantile 0.25 516142
Quantile 0.5 518680
Quantile 0.75 521192
Quantile 0.975 528922
Mean 373526
Stdev 3538.58
Quantile 0.025 366210
Quantile 0.25 371659
Quantile 0.5 373460
Quantile 0.75 375295
Quantile 0.975 381273
Mean 258267
Stdev 2448.2
Quantile 0.025 253175
Quantile 0.25 256980
Quantile 0.5 258229
Quantile 0.75 259495
Quantile 0.975 263598
Mean 237757
Stdev 2257
Quantile 0.025 233206
Quantile 0.25 236549
Quantile 0.5 237688
Quantile 0.75 238865
Quantile 0.975 242813
Mean 271205
Stdev 2571.93
Quantile 0.025 265908
Quantile 0.25 269845
Quantile 0.5 271152
Quantile 0.75 272487
Quantile 0.975 276857
Mean 296977
Stdev 2808.37
Quantile 0.025 290987
Quantile 0.25 295524
Quantile 0.5 296970
Quantile 0.75 298414
Quantile 0.975 302943
Mean 266733
Stdev 2530.83
Quantile 0.025 261566
Quantile 0.25 265388
Quantile 0.5 266671
Quantile 0.75 267986
Quantile 0.975 272339
Mean 355466
Stdev 3365
Quantile 0.025 348279
Quantile 0.25 353728
Quantile 0.5 355460
Quantile 0.75 357189
Quantile 0.975 362606
Mean 317179
Stdev 2998.02
Quantile 0.025 310941
Quantile 0.25 315602
Quantile 0.5 317134
Quantile 0.75 318688
Quantile 0.975 323700
Mean 196755
Stdev 1862.7
Quantile 0.025 192888
Quantile 0.25 195775
Quantile 0.5 196725
Quantile 0.75 197690
Quantile 0.975 200817
Mean 303291
Stdev 2872.28
Quantile 0.025 297186
Quantile 0.25 301803
Quantile 0.5 303278
Quantile 0.75 304756
Quantile 0.975 309416
Mean 256608
Stdev 2428.3
Quantile 0.025 251320
Quantile 0.25 255370
Quantile 0.5 256628
Quantile 0.75 257869
Quantile 0.975 261660
Mean 189886
Stdev 1799.11
Quantile 0.025 186201
Quantile 0.25 188932
Quantile 0.5 189845
Quantile 0.75 190780
Quantile 0.975 193858
Mean 234603
Stdev 2234.99
Quantile 0.025 230168
Quantile 0.25 233397
Quantile 0.5 234517
Quantile 0.75 235686
Quantile 0.975 239682
Mean 348646
Stdev 3294.49
Quantile 0.025 341430
Quantile 0.25 346971
Quantile 0.5 348683
Quantile 0.75 350365
Quantile 0.975 355456
Mean 843826
Stdev 8013.51
Quantile 0.025 825673
Quantile 0.25 839861
Quantile 0.5 844062
Quantile 0.75 848101
Quantile 0.975 859809
Mean 634943
Stdev 6014.36
Quantile 0.025 621505
Quantile 0.25 631932
Quantile 0.5 635075
Quantile 0.75 638124
Quantile 0.975 647118
Mean 357373
Stdev 3383.15
Quantile 0.025 350307
Quantile 0.25 355598
Quantile 0.5 357327
Quantile 0.75 359077
Quantile 0.975 364709
Mean 412938
Stdev 3908.93
Quantile 0.025 404706
Quantile 0.25 410900
Quantile 0.5 412903
Quantile 0.75 414920
Quantile 0.975 421347
Mean 321139
Stdev 3040.21
Quantile 0.025 314749
Quantile 0.25 319551
Quantile 0.5 321108
Quantile 0.75 322677
Quantile 0.975 327692
Mean 527163
Stdev 4987.38
Quantile 0.025 516379
Quantile 0.25 524607
Quantile 0.5 527185
Quantile 0.75 529740
Quantile 0.975 537615
Mean 425407
Stdev 4028.1
Quantile 0.025 417024
Quantile 0.25 423290
Quantile 0.5 425345
Quantile 0.75 427431
Quantile 0.975 434171
Mean 605794
Stdev 5734.75
Quantile 0.025 593470
Quantile 0.25 602843
Quantile 0.5 605800
Quantile 0.75 608742
Quantile 0.975 617889
Mean 452868
Stdev 4288.26
Quantile 0.025 443426
Quantile 0.25 450699
Quantile 0.5 452928
Quantile 0.75 455112
Quantile 0.975 461687
Mean 380472
Stdev 3601.76
Quantile 0.025 372790
Quantile 0.25 378609
Quantile 0.5 380462
Quantile 0.75 382313
Quantile 0.975 388125
Mean 556811
Stdev 5324.11
Quantile 0.025 544349
Quantile 0.25 554252
Quantile 0.5 557067
Quantile 0.75 559712
Quantile 0.975 567037
Mean 435093
Stdev 4119.22
Quantile 0.025 426045
Quantile 0.25 433005
Quantile 0.5 435145
Quantile 0.75 437244
Quantile 0.975 443587
Mean 417455
Stdev 3950.26
Quantile 0.025 408860
Quantile 0.25 415439
Quantile 0.5 417485
Quantile 0.75 419505
Quantile 0.975 425680
Mean 416683
Stdev 3940.5
Quantile 0.025 408300
Quantile 0.25 414640
Quantile 0.5 416667
Quantile 0.75 418695
Quantile 0.975 425075
Mean 233135
Stdev 2208.89
Quantile 0.025 228502
Quantile 0.25 231980
Quantile 0.5 233110
Quantile 0.75 234250
Quantile 0.975 237907
Mean 353634
Stdev 3356.43
Quantile 0.025 346117
Quantile 0.25 351959
Quantile 0.5 353712
Quantile 0.75 355410
Quantile 0.975 360415
Mean 213942
Stdev 2033.12
Quantile 0.025 209843
Quantile 0.25 212854
Quantile 0.5 213879
Quantile 0.75 214939
Quantile 0.975 218497
Mean 335122
Stdev 3167.03
Quantile 0.025 328290
Quantile 0.25 333495
Quantile 0.5 335132
Quantile 0.75 336757
Quantile 0.975 341773
Mean 232500
Stdev 2200.4
Quantile 0.025 227833
Quantile 0.25 231358
Quantile 0.5 232488
Quantile 0.75 233621
Quantile 0.975 237201
Mean 226446
Stdev 2142.97
Quantile 0.025 221972
Quantile 0.25 225322
Quantile 0.5 226418
Quantile 0.75 227526
Quantile 0.975 231094
Mean 293999
Stdev 2793.37
Quantile 0.025 288374
Quantile 0.25 292503
Quantile 0.5 293911
Quantile 0.75 295368
Quantile 0.975 300265
Mean 229571
Stdev 2175.26
Quantile 0.025 225065
Quantile 0.25 228425
Quantile 0.5 229533
Quantile 0.75 230660
Quantile 0.975 234325
Mean 371671
Stdev 3515.78
Quantile 0.025 364022
Quantile 0.25 369877
Quantile 0.5 371698
Quantile 0.75 373496
Quantile 0.975 378992
Mean 296524
Stdev 2810.66
Quantile 0.025 290749
Quantile 0.25 295036
Quantile 0.5 296463
Quantile 0.75 297923
Quantile 0.975 302713
Mean 292383
Stdev 2765.94
Quantile 0.025 286491
Quantile 0.25 290950
Quantile 0.5 292373
Quantile 0.75 293796
Quantile 0.975 298266
Mean 349361
Stdev 3308.08
Quantile 0.025 342437
Quantile 0.25 347629
Quantile 0.5 349320
Quantile 0.75 351030
Quantile 0.975 356520
Mean 620734
Stdev 5934.95
Quantile 0.025 606863
Quantile 0.25 617879
Quantile 0.5 621015
Quantile 0.75 623966
Quantile 0.975 632154
Mean 310084
Stdev 2944.73
Quantile 0.025 304116
Quantile 0.25 308513
Quantile 0.5 310001
Quantile 0.75 311534
Quantile 0.975 316651
Mean 328799
Stdev 3109.56
Quantile 0.025 322203
Quantile 0.25 327184
Quantile 0.5 328782
Quantile 0.75 330384
Quantile 0.975 335440
Mean 434868
Stdev 4114.53
Quantile 0.025 426246
Quantile 0.25 432715
Quantile 0.5 434821
Quantile 0.75 436947
Quantile 0.975 443760
Mean 669591
Stdev 6336.41
Quantile 0.025 655990
Quantile 0.25 666328
Quantile 0.5 669595
Quantile 0.75 672847
Quantile 0.975 682969
Mean 264142
Stdev 2498.32
Quantile 0.025 258907
Quantile 0.25 262834
Quantile 0.5 264113
Quantile 0.75 265404
Quantile 0.975 269541
Mean 386223
Stdev 3651.85
Quantile 0.025 378514
Quantile 0.25 384321
Quantile 0.5 386195
Quantile 0.75 388079
Quantile 0.975 394060
Mean 207198
Stdev 1975.68
Quantile 0.025 203304
Quantile 0.25 206127
Quantile 0.5 207115
Quantile 0.75 208150
Quantile 0.975 211714
Mean 496656
Stdev 4700.08
Quantile 0.025 486773
Quantile 0.25 494202
Quantile 0.5 496609
Quantile 0.75 499036
Quantile 0.975 506782
Mean 301637
Stdev 2854.52
Quantile 0.025 295489
Quantile 0.25 300170
Quantile 0.5 301644
Quantile 0.75 303107
Quantile 0.975 307643
Mean 198027
Stdev 1874.16
Quantile 0.025 194093
Quantile 0.25 197047
Quantile 0.5 198007
Quantile 0.75 198975
Quantile 0.975 202071
Mean 204224
Stdev 1932.67
Quantile 0.025 200160
Quantile 0.25 203214
Quantile 0.5 204204
Quantile 0.75 205202
Quantile 0.975 208388
Mean 295333
Stdev 2795.84
Quantile 0.025 289453
Quantile 0.25 293874
Quantile 0.5 295305
Quantile 0.75 296749
Quantile 0.975 301356
Mean 677934
Stdev 6521.96
Quantile 0.025 662386
Quantile 0.25 674859
Quantile 0.5 678321
Quantile 0.75 681530
Quantile 0.975 690181
Mean 382112
Stdev 3616.55
Quantile 0.025 374459
Quantile 0.25 380231
Quantile 0.5 382087
Quantile 0.75 383951
Quantile 0.975 389856
Mean 277321
Stdev 2621.95
Quantile 0.025 271643
Quantile 0.25 275978
Quantile 0.5 277335
Quantile 0.75 278678
Quantile 0.975 282806
Mean 216977
Stdev 2062.74
Quantile 0.025 212868
Quantile 0.25 215865
Quantile 0.5 216902
Quantile 0.75 217980
Quantile 0.975 221647
Mean 470373
Stdev 4455.16
Quantile 0.025 461034
Quantile 0.25 468043
Quantile 0.5 470322
Quantile 0.75 472623
Quantile 0.975 480002
Mean 247811
Stdev 2351.17
Quantile 0.025 242992
Quantile 0.25 246565
Quantile 0.5 247758
Quantile 0.75 248979
Quantile 0.975 253001
Mean 150895
Stdev 1447.99
Quantile 0.025 148114
Quantile 0.25 150100
Quantile 0.5 150816
Quantile 0.75 151577
Quantile 0.975 154278
Mean 365840
Stdev 3458.32
Quantile 0.025 358416
Quantile 0.25 364058
Quantile 0.5 365842
Quantile 0.75 367618
Quantile 0.975 373139
Mean 408327
Stdev 3865.44
Quantile 0.025 400020
Quantile 0.25 406339
Quantile 0.5 408332
Quantile 0.75 410315
Quantile 0.975 416479
Mean 648146
Stdev 6190.89
Quantile 0.025 633747
Quantile 0.25 645155
Quantile 0.5 648421
Quantile 0.75 651506
Quantile 0.975 660129
Mean 407382
Stdev 3857.88
Quantile 0.025 399323
Quantile 0.25 405360
Quantile 0.5 407330
Quantile 0.75 409325
Quantile 0.975 415746
Mean 295189
Stdev 2793.54
Quantile 0.025 289248
Quantile 0.25 293741
Quantile 0.5 295177
Quantile 0.75 296615
Quantile 0.975 301141
Mean 228828
Stdev 2167.1
Quantile 0.025 224274
Quantile 0.25 227696
Quantile 0.5 228806
Quantile 0.75 229924
Quantile 0.975 233500
Mean 210055
Stdev 1989.1
Quantile 0.025 205919
Quantile 0.25 209009
Quantile 0.5 210024
Quantile 0.75 211054
Quantile 0.975 214387
Mean 233774
Stdev 2212.22
Quantile 0.025 229044
Quantile 0.25 232632
Quantile 0.5 233771
Quantile 0.75 234908
Quantile 0.975 238463
Mean 311807
Stdev 2952.97
Quantile 0.025 305705
Quantile 0.25 310248
Quantile 0.5 311752
Quantile 0.75 313283
Quantile 0.975 318275
Mean 246040
Stdev 2330.45
Quantile 0.025 241158
Quantile 0.25 244821
Quantile 0.5 246012
Quantile 0.75 247216
Quantile 0.975 251079
Mean 259833
Stdev 2461.64
Quantile 0.025 254662
Quantile 0.25 258548
Quantile 0.5 259807
Quantile 0.75 261078
Quantile 0.975 265142
Mean 297455
Stdev 2814.71
Quantile 0.025 291569
Quantile 0.25 295980
Quantile 0.5 297419
Quantile 0.75 298875
Quantile 0.975 303551
Mean 402797
Stdev 3805.35
Quantile 0.025 394723
Quantile 0.25 400820
Quantile 0.5 402777
Quantile 0.75 404738
Quantile 0.975 410921
Mean 434390
Stdev 4113.79
Quantile 0.025 425801
Quantile 0.25 432233
Quantile 0.5 434334
Quantile 0.75 436462
Quantile 0.975 443314
Mean 360627
Stdev 3412.75
Quantile 0.025 353279
Quantile 0.25 358873
Quantile 0.5 360634
Quantile 0.75 362384
Quantile 0.975 367810
Mean 466702
Stdev 4413.83
Quantile 0.025 457345
Quantile 0.25 464409
Quantile 0.5 466677
Quantile 0.75 468951
Quantile 0.975 476135
Mean 356191
Stdev 3370.17
Quantile 0.025 348879
Quantile 0.25 354467
Quantile 0.5 356211
Quantile 0.75 357936
Quantile 0.975 363229
Mean 292833
Stdev 2770.2
Quantile 0.025 287007
Quantile 0.25 291386
Quantile 0.5 292805
Quantile 0.75 294236
Quantile 0.975 298799
Mean 277182
Stdev 2630.17
Quantile 0.025 271877
Quantile 0.25 275773
Quantile 0.5 277101
Quantile 0.75 278474
Quantile 0.975 283071
Mean 301676
Stdev 2852.79
Quantile 0.025 295589
Quantile 0.25 300200
Quantile 0.5 301668
Quantile 0.75 303136
Quantile 0.975 307734
Mean 230228
Stdev 2178.82
Quantile 0.025 225650
Quantile 0.25 229090
Quantile 0.5 230206
Quantile 0.75 231331
Quantile 0.975 234926
Mean 367919
Stdev 3483.05
Quantile 0.025 360409
Quantile 0.25 366131
Quantile 0.5 367929
Quantile 0.75 369714
Quantile 0.975 375241
Mean 363906
Stdev 3446.51
Quantile 0.025 356755
Quantile 0.25 362091
Quantile 0.5 363848
Quantile 0.75 365634
Quantile 0.975 371427
Mean 466630
Stdev 4413.7
Quantile 0.025 457314
Quantile 0.25 464330
Quantile 0.5 466595
Quantile 0.75 468872
Quantile 0.975 476103
Mean 320721
Stdev 3037.91
Quantile 0.025 314308
Quantile 0.25 319139
Quantile 0.5 320696
Quantile 0.75 322262
Quantile 0.975 327243
Mean 294165
Stdev 2785.99
Quantile 0.025 288354
Quantile 0.25 292703
Quantile 0.5 294126
Quantile 0.75 295567
Quantile 0.975 300215
Mean 412564
Stdev 3903.79
Quantile 0.025 404082
Quantile 0.25 410571
Quantile 0.5 412592
Quantile 0.75 414588
Quantile 0.975 420704
Mean 335962
Stdev 3198.11
Quantile 0.025 329572
Quantile 0.25 334242
Quantile 0.5 335849
Quantile 0.75 337519
Quantile 0.975 343186
Mean 436743
Stdev 4135.81
Quantile 0.025 428036
Quantile 0.25 434586
Quantile 0.5 436704
Quantile 0.75 438838
Quantile 0.975 445644
Mean 312571
Stdev 2955.81
Quantile 0.025 306260
Quantile 0.25 311043
Quantile 0.5 312565
Quantile 0.75 314085
Quantile 0.975 318843
Mean 855744
Stdev 8098.09
Quantile 0.025 838334
Quantile 0.25 851578
Quantile 0.5 855756
Quantile 0.75 859910
Quantile 0.975 872815
Mean 578983
Stdev 5475.27
Quantile 0.025 567194
Quantile 0.25 576167
Quantile 0.5 578995
Quantile 0.75 581803
Quantile 0.975 590505
Mean 637345
Stdev 6023.27
Quantile 0.025 624339
Quantile 0.25 634253
Quantile 0.5 637367
Quantile 0.75 640456
Quantile 0.975 649982
Mean 358542
Stdev 3389.33
Quantile 0.025 351269
Quantile 0.25 356795
Quantile 0.5 358544
Quantile 0.75 360285
Quantile 0.975 365698
Mean 212846
Stdev 2015.09
Quantile 0.025 208642
Quantile 0.25 211789
Quantile 0.5 212818
Quantile 0.75 213861
Quantile 0.975 217220
Mean 286188
Stdev 2710.27
Quantile 0.025 280423
Quantile 0.25 284785
Quantile 0.5 286177
Quantile 0.75 287571
Quantile 0.975 291963
Mean 234496
Stdev 2231.38
Quantile 0.025 230056
Quantile 0.25 233292
Quantile 0.5 234412
Quantile 0.75 235579
Quantile 0.975 239554
Mean 383040
Stdev 3626.01
Quantile 0.025 375258
Quantile 0.25 381172
Quantile 0.5 383041
Quantile 0.75 384902
Quantile 0.975 390697
Mean 324741
Stdev 3080.7
Quantile 0.025 318419
Quantile 0.25 323109
Quantile 0.5 324673
Quantile 0.75 326272
Quantile 0.975 331534
Mean 486125
Stdev 4603.16
Quantile 0.025 476549
Quantile 0.25 483705
Quantile 0.5 486054
Quantile 0.75 488437
Quantile 0.975 496145
Mean 480571
Stdev 4547.79
Quantile 0.025 470881
Quantile 0.25 478217
Quantile 0.5 480556
Quantile 0.75 482895
Quantile 0.975 490244
Mean 414111
Stdev 3918.02
Quantile 0.025 405820
Quantile 0.25 412074
Quantile 0.5 414085
Quantile 0.75 416105
Quantile 0.975 422500
Mean 529394
Stdev 5014.84
Quantile 0.025 518297
Quantile 0.25 526866
Quantile 0.5 529477
Quantile 0.75 532026
Quantile 0.975 539654
Mean 331753
Stdev 3143.38
Quantile 0.025 325166
Quantile 0.25 330109
Quantile 0.5 331716
Quantile 0.75 333339
Quantile 0.975 338549
Mean 578905
Stdev 5490.21
Quantile 0.025 566523
Quantile 0.25 576177
Quantile 0.5 579054
Quantile 0.75 581827
Quantile 0.975 589907
Mean 437235
Stdev 4142.23
Quantile 0.025 428200
Quantile 0.25 435126
Quantile 0.5 437271
Quantile 0.75 439386
Quantile 0.975 445840
Mean 371464
Stdev 3521.07
Quantile 0.025 364092
Quantile 0.25 369622
Quantile 0.5 371421
Quantile 0.75 373239
Quantile 0.975 379084
Mean 182946
Stdev 1738.82
Quantile 0.025 179477
Quantile 0.25 182009
Quantile 0.5 182883
Quantile 0.75 183793
Quantile 0.975 186878
Mean 239777
Stdev 2270.53
Quantile 0.025 235078
Quantile 0.25 238580
Quantile 0.5 239737
Quantile 0.75 240914
Quantile 0.975 244743
Mean 326498
Stdev 3089.13
Quantile 0.025 320094
Quantile 0.25 324870
Quantile 0.5 326445
Quantile 0.75 328047
Quantile 0.975 333243
Mean 831117
Stdev 7864.51
Quantile 0.025 814012
Quantile 0.25 827103
Quantile 0.5 831176
Quantile 0.75 835197
Quantile 0.975 847499
Mean 373227
Stdev 3548.57
Quantile 0.025 366041
Quantile 0.25 371333
Quantile 0.5 373124
Quantile 0.75 374971
Quantile 0.975 381149
Mean 266562
Stdev 2526.48
Quantile 0.025 261296
Quantile 0.25 265236
Quantile 0.5 266525
Quantile 0.75 267831
Quantile 0.975 272052
Mean 825819
Stdev 7845.03
Quantile 0.025 808013
Quantile 0.25 821944
Quantile 0.5 826059
Quantile 0.75 830010
Quantile 0.975 841433
Mean 509030
Stdev 4821.72
Quantile 0.025 498998
Quantile 0.25 506496
Quantile 0.5 508956
Quantile 0.75 511451
Quantile 0.975 519525
Mean 388967
Stdev 3681.94
Quantile 0.025 380957
Quantile 0.25 387088
Quantile 0.5 388994
Quantile 0.75 390876
Quantile 0.975 396636
Mean 597720
Stdev 5657.37
Quantile 0.025 585451
Quantile 0.25 594827
Quantile 0.5 597754
Quantile 0.75 600648
Quantile 0.975 609541
Mean 473603
Stdev 4480.68
Quantile 0.025 464105
Quantile 0.25 471276
Quantile 0.5 473577
Quantile 0.75 475885
Quantile 0.975 483180
Mean 366464
Stdev 3468.74
Quantile 0.025 359202
Quantile 0.25 364647
Quantile 0.5 366421
Quantile 0.75 368214
Quantile 0.975 373969
Mean 286265
Stdev 2708.93
Quantile 0.025 280466
Quantile 0.25 284867
Quantile 0.5 286262
Quantile 0.75 287654
Quantile 0.975 292000
Mean 373413
Stdev 3530.52
Quantile 0.025 365946
Quantile 0.25 371576
Quantile 0.5 373389
Quantile 0.75 375209
Quantile 0.975 380975
Mean 909492
Stdev 8614.66
Quantile 0.025 890310
Quantile 0.25 905169
Quantile 0.5 909664
Quantile 0.75 914036
Quantile 0.975 926998
Mean 934776
Stdev 8867.93
Quantile 0.025 914881
Quantile 0.25 930354
Quantile 0.5 934989
Quantile 0.75 939475
Quantile 0.975 952654
Mean 326115
Stdev 3087.76
Quantile 0.025 319589
Quantile 0.25 324509
Quantile 0.5 326092
Quantile 0.75 327684
Quantile 0.975 332735
Mean 301979
Stdev 2857.7
Quantile 0.025 295887
Quantile 0.25 300500
Quantile 0.5 301971
Quantile 0.75 303440
Quantile 0.975 308054
Mean 356438
Stdev 3374.24
Quantile 0.025 349339
Quantile 0.25 354677
Quantile 0.5 356405
Quantile 0.75 358147
Quantile 0.975 363704
Mean 252545
Stdev 2389.69
Quantile 0.025 247546
Quantile 0.25 251293
Quantile 0.5 252516
Quantile 0.75 253751
Quantile 0.975 257718
Mean 561542
Stdev 5323.17
Quantile 0.025 550616
Quantile 0.25 558722
Quantile 0.5 561425
Quantile 0.75 564190
Quantile 0.975 573275
Mean 331164
Stdev 3148.68
Quantile 0.025 324882
Quantile 0.25 329468
Quantile 0.5 331051
Quantile 0.75 332697
Quantile 0.975 338284
Mean 583450
Stdev 5521.82
Quantile 0.025 571513
Quantile 0.25 580620
Quantile 0.5 583473
Quantile 0.75 586301
Quantile 0.975 595025
Mean 420332
Stdev 3997.38
Quantile 0.025 412350
Quantile 0.25 418180
Quantile 0.5 420189
Quantile 0.75 422278
Quantile 0.975 429365
Mean 240976
Stdev 2277.97
Quantile 0.025 236110
Quantile 0.25 239799
Quantile 0.5 240972
Quantile 0.75 242144
Quantile 0.975 245807
Mean 432884
Stdev 4096.63
Quantile 0.025 424172
Quantile 0.25 430761
Quantile 0.5 432867
Quantile 0.75 434975
Quantile 0.975 441614
Mean 346847
Stdev 3279.92
Quantile 0.025 339811
Quantile 0.25 345156
Quantile 0.5 346848
Quantile 0.75 348532
Quantile 0.975 353775
Mean 328484
Stdev 3108.59
Quantile 0.025 321867
Quantile 0.25 326874
Quantile 0.5 328472
Quantile 0.75 330072
Quantile 0.975 335102
Mean 383059
Stdev 3631.04
Quantile 0.025 374997
Quantile 0.25 381234
Quantile 0.5 383126
Quantile 0.75 384969
Quantile 0.975 390462
Mean 295699
Stdev 2796.11
Quantile 0.025 289617
Quantile 0.25 294271
Quantile 0.5 295720
Quantile 0.75 297150
Quantile 0.975 301522
Mean 435337
Stdev 4118.37
Quantile 0.025 426360
Quantile 0.25 433238
Quantile 0.5 435373
Quantile 0.75 437478
Quantile 0.975 443896
Mean 404180
Stdev 3825.2
Quantile 0.025 395739
Quantile 0.25 402248
Quantile 0.5 404239
Quantile 0.75 406186
Quantile 0.975 412028
Mean 222164
Stdev 2112.26
Quantile 0.025 217930
Quantile 0.25 221030
Quantile 0.5 222093
Quantile 0.75 223195
Quantile 0.975 226921
Mean 435177
Stdev 4116.79
Quantile 0.025 426411
Quantile 0.25 433044
Quantile 0.5 435162
Quantile 0.75 437280
Quantile 0.975 443937
Mean 340632
Stdev 3221.24
Quantile 0.025 333699
Quantile 0.25 338975
Quantile 0.5 340638
Quantile 0.75 342291
Quantile 0.975 347413
Mean 209792
Stdev 1988.85
Quantile 0.025 205712
Quantile 0.25 208738
Quantile 0.5 209747
Quantile 0.75 210780
Quantile 0.975 214178
Mean 230917
Stdev 2187.32
Quantile 0.025 226303
Quantile 0.25 229778
Quantile 0.5 230898
Quantile 0.75 232026
Quantile 0.975 235616
Mean 185011
Stdev 1755.15
Quantile 0.025 181454
Quantile 0.25 184073
Quantile 0.5 184961
Quantile 0.75 185875
Quantile 0.975 188925
Mean 171521
Stdev 1630.18
Quantile 0.025 168245
Quantile 0.25 170647
Quantile 0.5 171468
Quantile 0.75 172318
Quantile 0.975 175184
Mean 454831
Stdev 4305.83
Quantile 0.025 445296
Quantile 0.25 452661
Quantile 0.5 454904
Quantile 0.75 457094
Quantile 0.975 463632
Mean 326896
Stdev 3094.96
Quantile 0.025 320477
Quantile 0.25 325266
Quantile 0.5 326844
Quantile 0.75 328448
Quantile 0.975 333651
Mean 471450
Stdev 4471.21
Quantile 0.025 462342
Quantile 0.25 469070
Quantile 0.5 471334
Quantile 0.75 473661
Quantile 0.975 481374
Mean 501761
Stdev 4754.61
Quantile 0.025 491918
Quantile 0.25 499255
Quantile 0.5 501676
Quantile 0.75 504140
Quantile 0.975 512159
Mean 220686
Stdev 2089.17
Quantile 0.025 216384
Quantile 0.25 219580
Quantile 0.5 220643
Quantile 0.75 221728
Quantile 0.975 225276
Mean 297517
Stdev 2819.58
Quantile 0.025 291713
Quantile 0.25 296025
Quantile 0.5 297459
Quantile 0.75 298922
Quantile 0.975 303715
Mean 299751
Stdev 2839.25
Quantile 0.025 293805
Quantile 0.25 298265
Quantile 0.5 299716
Quantile 0.75 301183
Quantile 0.975 305893
Mean 438600
Stdev 4150.94
Quantile 0.025 429796
Quantile 0.25 436445
Quantile 0.5 438576
Quantile 0.75 440714
Quantile 0.975 447468
Mean 330588
Stdev 3129.29
Quantile 0.025 323783
Quantile 0.25 328991
Quantile 0.5 330611
Quantile 0.75 332211
Quantile 0.975 337109
Mean 312533
Stdev 2956.49
Quantile 0.025 306312
Quantile 0.25 310989
Quantile 0.5 312504
Quantile 0.75 314031
Quantile 0.975 318897
Mean 253925
Stdev 2408.26
Quantile 0.025 249004
Quantile 0.25 252645
Quantile 0.5 253866
Quantile 0.75 255118
Quantile 0.975 259256
Mean 1134268
Stdev 10908.1
Quantile 0.025 1108288
Quantile 0.25 1129119
Quantile 0.5 1134908
Quantile 0.75 1140279
Quantile 0.975 1154776
Mean 267731
Stdev 2532.04
Quantile 0.025 262259
Quantile 0.25 266433
Quantile 0.5 267742
Quantile 0.75 269039
Quantile 0.975 273039
Mean 309730
Stdev 2929.91
Quantile 0.025 303562
Quantile 0.25 308201
Quantile 0.5 309703
Quantile 0.75 311215
Quantile 0.975 316034 # Posterior mean and 95% CI
mn_data$PMoriginal <- sapply(marginals_summaries, '[[', "mean")
mn_data$LLoriginal <- sapply(marginals_summaries, '[[', "quant0.025")
mn_data$ULoriginal <- sapply(marginals_summaries, '[[', "quant0.975")
# common legend
at <- seq(min(c(mn_data$PMoriginal, mn_data$LLoriginal, mn_data$ULoriginal)),
max(c(mn_data$PMoriginal, mn_data$LLoriginal, mn_data$ULoriginal)),
length.out = 8)
# popup table
popuptable <- leafpop::popupTable(dplyr::mutate_if(mn_data,
is.numeric, round, digits = 2),
zcol = c("NAME", "vble", "HouseholdSizeE", "IncomeE", "PM", "LL", "UL"),
row.numbers = FALSE, feature.id = FALSE)
m1 <- mapview(mn_data, zcol = "PMoriginal",
map.types = "CartoDB.Positron",
at = at, popup = popuptable)
m2 <- mapview(mn_data, zcol = "LLoriginal",
map.types = "CartoDB.Positron",
at = at, popup = popuptable)
m3 <- mapview(mn_data, zcol = "ULoriginal",
map.types = "CartoDB.Positron",
at = at, popup = popuptable)
leafsync::sync(m1, m2, m3, ncol = 3)Conclusion